PID controllers are widely used and adaptable to various types of systems. However, for the response to be adequate under different conditions, the PID gains must be adjusted. The tuning is made according to the difference between the reference value and the real value (error). This work presents a selfadjusting PID controller based on a backpropagation artificial neural network. The network calculates the appropriate gains according to the desired output, that is, the dynamic response desired which is composed of the transient part and the stationary part of the step response of a system. The contribution of the work is that in addition to using the error for network training, the maximum desired values of overshoots, settling times, and stationary errors were used as input data for the network. An offline training database was created using genetic algorithms to obtain the dynamic response data associated with PID gains. The genetic algorithm allows getting data in different operating ranges and allows using only stable gains combinations. The database was used for training. Subsequently, the neural network estimates an appropriate gain combination, adapting to the error and the desired response. The method performance is evaluated by controlling the speed of a direct current motor. The results indicate an average error of 4% for the database between the requested and system response. On the other hand, the gains estimated by the network in the test dataset (1544 combinations) did not cause instability and complying with the expected dynamic response in 86% of the dataset.

Backstepping is a control technique based on Lyapunov’s theory that has been successfully implemented in the control of motors and robots by several nonlinear methods. However, there are no standardized methods for tuning control gains (unlike the PIDs). This paper shows the tuning gains of the backstepping controller, using Genetic Algorithms (GA), for an Unmanned Aerial Vehicle (UAV), quadrotor type, designed for autonomous trajectory tracking. First, a dynamic model of the vehicle is obtained through the Newton‒Euler methodology. Then, the control law is obtained, and self-tuning is performed, through which we can obtain suitable values of the gains in order to achieve the design requirements. In this work, the establishment time and maximum impulse are considered as such. The tuning and simulations of the system response were performed using the MATLAB-Simulink environment, obtaining as a result the compliance of the design parameters and the correct tracking of different trajectories. The results show that self-tuning by means of genetic algorithms satisfactorily adjusts for the gains of a backstepping controller applied to a quadrotor and allows for the implementation of a control system that responds appropriately to errors of different magnitude.

The direct current (DC) motors are widely used; therefore, they are subject to multiple studies, different control techniques or analyses require a dynamic DC motor model. The parameters are needed to complete the model, which can be challenging to obtain. Therefore, multiple parametric estimation techniques have been developed. This paper presents a metaheuristic cuckoo search algorithm modified for motors as a parametric estimation tool. A cost function is based on the current and velocity error obtained when an input voltage step is applied to the motor. The main difference with similar works is that we used the steady-state equations to determine the parameters. The algorithm proposed is compared with the Steiglitz-McBride and the original cuckoo search algorithms to evaluate its performance objectively. Simulated and experimental results show that the algorithm proposed can calculate the parameters with better accuracy than the original cuckoo search and Steiglitz-McBride. The modifications made to the original algorithm of the cuckoo search allowed finding the values of the parameters motor with a root mean square error of less than 0.1% for signals obtained with simulation and less than 1% for real signals sampled at 0.001 s.

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